A317964 Prime numbers in the lexicographically earliest sequence of positive integers whose prime indices are not already in the sequence (A304360).

2, 5, 13, 17, 23, 31, 37, 43, 47, 61, 67, 73, 79, 89, 103, 107, 109, 113, 137, 149, 151, 163, 167, 179, 181, 193, 197, 223, 227, 233, 241, 251, 257, 263, 269, 271, 277, 281, 307, 317, 347, 349, 353, 359, 379, 383, 389, 397, 419, 421, 431, 433, 449, 457, 463, 467, 487, 499, 503, 509, 521, 523, 547

Offset: 1

Author

N. J. A. Sloane, Aug 26 2018

Keywords

• nonn

Comments

Also primes whose prime index is not in A304360, or is in A324696. A prime index of n is a number m such that prime(m) divides n. - Gus Wiseman, Mar 19 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A001462, A007097, A060197, A079254, A112798, A276625, A277098, A290822, A304360, A306844.

Cf. A324695, A324698, A324704, A324741, A324756, A324758, A324765, A324766, A324768.

Programs

Maple

count:= 0:
P:= {}: A:= NULL:
for n from 2 while count < 100 do
  pn:= numtheory:-factorset(n);
  if pn intersect P = {} then
    P:= P union {ithprime(n)};
    if isprime(n) then A:= A, n; count:= count+1 fi;
  fi
od:
A; # Robert Israel, Aug 26 2018

Mathematica

aQ[n_]:=n==1||Or@@Cases[FactorInteger[n],{p_,_}:>!aQ[PrimePi[p]]];
Prime[Select[Range[100],aQ]] (* Gus Wiseman, Mar 19 2019 *)